What is Time and Space

Cool!!! Just noticed Raphael's name in the references of the Wikipedia piece. Raph, whilst studying part III, came out of one of my black hole tutorials and said "#####, that was the best lecture I've ever had" Later we shared an office for a few years. Oh, it takes me back...

No, not at all. It's just a deeper level of the maths/physics. I can get twitchy when people start using qm/gr as entrances to the metaphysical, as Randman is doing. There is nothing mysterious about QM when looked at mathematically. My personal position is that there is not a single stroke of evidence for God in the physical universe. A perfect artist doesn't leave brush strokes... or a perfect watchmaker, scratches...

You're quite right, I am! I am a Christian, and my church is a sort of pentecostal/Vineyard/Hillsong hybrid, so I can hardly avoid it But I am convinced that QM does not hold any key to spirituality or the spiritual. In my view, God can interact with any part of creation at any level.Quantum theory really isn't that mysterious, but unfortunately that's a view built upon many years experience in the field and is very difficult to convey. Most people outside of the field have this idea of uncertainty and probability. But QM is totally deterministic. The evolution of a wave-function is purely a function of its initial conditions. It is only a "measurement" of the wave-function that introduces any sense of probability or uncertainty.Furthermore, QM is totally causal, as in doesn't allow for FTL communication. Entanglement seems mysterious but that is from the perspective of large scale physics. From the mathematics, it makes total sense. As with GR, its mysteriousness stems from the mistake of comparing it with our observed everyday "reality". This is where all of the layman accounts (New Scientist, etc) get their mileage: ooh, isn't it different to everyday life!!!

A quick addendum... this is a slippery argument and is tantamount to a god of the gaps. I have personally heard preachers announce that God upholds the universe by preventing nuclei from exploding from electrostatic repulsion. Well, in the long run I guess this is true and God's mechanism is known as the strong nuclear force... but this is not what they meant. A place for God has always been found in the next level of physical mystery, but He soon gets evicted as understanding dawns...

Hmmm, you should realise now that this is mubo-jumbo. This is the language of New Scientist: conveys nothing, and if used as a basis for further musings it will rapidly leads you into crank territory Remember, space is only a slice of reality... a "string" is a slice of a tube. It is the network of tubes, splitting and rejoining that creates the tapestry of string-theory. We are now talking about a highly convoluted two-dimensional surface. String theory is about the geometry and topology of this surface, and of the mathematical fields defined on this surface... it most certainly is not about "minute bits of energy".

Hmmm, I'm not so sure. Greene will talk about loops of string, he's a particle physicist But you should see some string world-sheets (tubes) Look out for "pairs of pants"... it's what the universe rests upon Yes, I largelt agree with this. The background independent approach to string theory was an area in which I spent some time. It is really a formalism of my idea of space-time being a projection. Actually, I prefer the idea of "emergent concept" than projection. Projection, as Son Goku pointed out, is more the domain of the Holographic Principle. Absolutely.

I'm not sure what's being said here. Can you quote a little more from around this comment?

This is known as the Holographic Principle, and the idea is that all of 3d reality can be contained on a 2d surface. In other words, 3d reality is a projection of a 2d image. No, the opposite. It points us to a lower dimensional reality! And this is also the case in string theory. Despite all the talk of "extra dimensions", string theory is actually just concerned with two dimensions! But this is now getting technical...I know why you're thinking along the line of phasors, and there are some connections (as you mention, adding vectors is not straightforward) but primarily the answer is no. It is potentially possible to create anti-gravity, but you are right... it is not easy. Casimir energy appears to be one way, though it is wholly undemonstrated that it would work. Yes, for an appreciable amount of negative enrgy-density you would need a very large volume of space.

True, but they don't have much choice in the matter They are stuck with the brush strokes themselves. They can use that to increase of their art if they have the ability and the desire. I don't see it as hiding things. I just think that the creation is a contained whole, and that there is no "knot in the balloon" to find.

It's a long time since Part III for me. At the time it was incredible. I would still describe it as possibly the best year of my life; I have never worked so hard, nor achieved so much. My Part III notes take up more room than my degree! I came to Part III as a physicist and expected to fail... I left as a mathematician. If it's anything like it was, then I would certainly recommend it. There are probably good (and cheaper!) alternatives now, but that wasn't really the case then. The lecturing was fairly poor, as with most of the maths Tripos at the time. But then it sometimes made up for it with the excellent quality of the tutors

Both, but the mathematics that will lead us to more fundemental understanding will be that of the projecting world. One way of thinking about this (for the computer literate) is the difference between raster and vector graphics. We usually imagine the universe as a raster graphic bit-map... there is a background (space-time) and at certain locations, there are particles (bits set to be on) and at other places there are no particles (bits off). This idea of a projection is more like vector graphics. There is a particle at one particular "location", and a 2nd at another "location". There is no concept of anything being between the particles, although a "distance" can be defined based upon the two "locations". Hmmm, this is a bit fuzzy at the moment... I need to work on this analogy, but I think it has merit.

Yes, you are There are no hidden variables as such. If you are thinking of Hilbert space (infinite dimensional) then this is very different to the dimensions of space-time>And I'm not saying that there aren't higher dimensiosn - I'm fairly convinced that there are - just that all of these dimensions are possibly just a projection or an emergent concept from a low (2?) dimensional (nehind the scenes) reality.

Well, at the moment it is just background independent string theory... a 2d geometry in the form of a network of interconnecting tubes. It is the surface of the tubes that is reality. There is no inside or outside of the tubes, other than that used by us to picture what's going on.

yesterday's metaphysics is today's physics... just think of relatvistic and quantum concepts presented to the scientists of the 1850s! The old story What you have to remember is that just about all 20th C particle/quantum/relativistic physics proceeded in precisely this way to staggering success... so much so that there was real suspicion that something very odd was going on.How many "oh well, it's a very nice piece of mathematics but what has it got to do with reality?" were followed by "err, ok, err, wow!"?Let's see... the whole of GR obviously; negative energy solutions of Dirac equation leading to prediction of anti-matter; the hadron/meson multiplet spectrum via group theory; and probably the most amazing and best example: Yang-Mills non-Abelian gauge theory leading to ElectroWeak and QCD. And that's just off the top of my head.You can start to see why we don't have a huge amount of patience for comments such as "it is merely a framework to be used for studying reality".No-one is saying that any of these "frameworks" are reality-incarnate, but to ignore mathematical implications in these theories is to stick one's head in the sand.As an aside:Turning it around, the mathematical physics that comes out of such research can reveal itself to be better at mathematics than the original pure mathematicians! Take Witten's topological field theory and its relation to Morse Theory and its ability to generate Donaldson Invariants in a hundredth of the time it takes Donaldson (won Witten the Field's Medal... first physicist to win it I think). The bizarre implications are hard to grasp here and easily missed, but I can talk about this further if anyone is interested.

Yep Exactly. Our amazing theory of the universe which works to a degree unparalleled in physics yet tells us that time is nothing special. Yet we know damn well it is... the ability to know depends upon it! This actually has an official name "The Problem of Time". The problem is that the heat equation is only valid in the non-relativistic regime. It only makes sense at our scale, it is not a universal of the universe. For example, Schrodinger's Equation is just a version of the heat equation, but is of limited use. It is abandoned as soon as relativistic considerations are taken into account and replaced by the Dirac and Klein-Gordon Equations (amongst some others) which all treat space and time equivalently. Our fundemental understanding of matter, quantum field theory, is wholely based upon the equivalence of space and time.You can see why we call this a "problem". The deeper we go, the less we understand about our relation to time!It appears that time-flow is an emergent feature of the universe, not a fundemental property. Replace "illusion" with "emergent property" and you pretty much have our current understanding. I don't think "illusion" is too far off the mark. The "flow" seems to require a conciousness to exist to appreciate it. Other than for conciousness, everything is just a static 4 dimensional construct as General Relativity has told us for the past 100 years...